Question

Find the derivative of f(x) = 2x^2 - 4x +3

Answer 1

Step-by-step explanation

`2x^2-4x+3`

When taking derivatives of polynomials, we primarily make use of the power rule.

Power rule.

`\begin{gathered} f(x)=x^n \\ \text{then} \\ f^(\prime)(x)=nx^(n-1) \end{gathered}`

also, the derivate of a sum is the sum of the derivates

hence

`\begin{gathered} g(x)=f(x)+h(x)+\ldots z(x) \\ g^(\prime)(x)=f^(\prime)(x)+h^(\prime)(x)+\ldots.z^(\prime)(x) \end{gathered}`

Step 1

apply:

`\begin{gathered} f(x)=2x^2-4x+3 \\ f^(\prime)(x)=2\cdot2x^(2-1)-4(1)x^(1-1)+ \\ f^(\prime)(x)=4x^{}-4(1)x^0+3^0 \\ f^(\prime)(x)=4x^{}-4(1)(1) \\ f^(\prime)(x)=4z-4 \end{gathered}`

therefore, the answer is